Finite Group Databasebeta

← C131×#10286 #45696170

Subgroups — C131×#10286 #45696170

Order 33536.

542 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3227×C131C211yesmaximal, characteristic
2#3226×C131C211yesmaximal, characteristic
3#2862×C131C211yesmaximal, characteristic, complemented
4#1962×C131C211yesmaximal, characteristic
5#1549×C131C211yesmaximal, characteristic, complemented
6#1546×C131C211yesmaximal, characteristic, complemented
7#1276×C131C211yesmaximal, characteristic, complemented
8#532×C131C2211yescharacteristic
9C2×C4⋊Q8×C131C2211yescharacteristic
10C2×C4⋊Q8×C131C2211yescharacteristic
11#500×C131—21no—
12#498×C131—21no—
13#486×C131—21no—
14#486×C131—21no—
15#481×C131—22no—
16#480×C131—22no—
17#476×C131—22no—
18#474×C131—22no—
19#431×C131C2211yescharacteristic
20#431×C131C2211yescharacteristic
21#423×C131C2211yescharacteristic
22C2×#104×C131—22no—
23#391×C131—22no—
24#391×C131—22no—
25#382×C131—22no—
26C43×C131C2211yescharacteristic
27#332×C131—22no—
28#332×C131—22no—
29C2×#41×C131—21no—
30C22×Q8×C131—21no—
31C22×Q8×C131—21no—
32C2×M16×C131—21no—
33C4⋊Q8×C131—21no—
34C4⋊Q8×C131—21no—
35C4⋊Q8×C131—21no—
36C4⋊Q8×C131—21no—
37C4⋊Q8×C131—21no—
38C4⋊Q8×C131—21no—
39C4⋊Q8×C131—21no—
40C4⋊Q8×C131—21no—
41C4⋊Q8×C131D411yescharacteristic
42#127×C131D411yescharacteristic
43#124×C131—21no—
44#121×C131—21no—
45#121×C131—21no—
46C4×D4×C131—21no—
47C4×D4×C131—21no—
48C2×C4⋊C4×C131—21no—
49C2×C4⋊C4×C131—21no—
50C2×C4⋊C4×C131D412yes—
51C2×C4⋊C4×C131D412yes—
52C2×C42×C131—21no—
53C2×C42×C131—21no—
54C2×C42×C131D412yes—
55C2×C42×C131C2311yescharacteristic
56#107×C131—24no—
57#106×C131—24no—
58C4⋊C8×C131—21no—
59C4⋊C8×C131—21no—
60C4⋊C8×C131D412yes—
61C4⋊C8×C131D412yes—
62#104×C131—44no—
63#102×C131—24no—
64#102×C131—24no—
65C22⋊C8×C131—21no—
66C22⋊C8×C131—21no—
67C4×C8×C131—21no—
68C4×C8×C131—21no—
69#95×C131—28no—
70#41×C131—42no—
71#41×C131—42no—
72C2×Q8×C131—21no—
73C2×Q8×C131—44no—
74C2×Q8×C131—41no—
75C2×Q8×C131—41no—
76C2×Q8×C131—41no—
77C2×Q8×C131—41no—
78C2×Q8×C131—42no—
79C2×Q8×C131—42no—
80C2×D4×C131—21no—
81C2×D4×C131—21no—
82C2×D4×C131—21no—
83C2×D4×C131—41no—
84C22×C4×C131—22no—
85C22×C4×C131—22no—
86C22×C4×C131—22no—
87C22×C4×C131—41no—
88C22×C4×C131C2×D411yescharacteristic
89C22×C4×C131C2×D411yescharacteristic
90C22×C4×C131C2×D411yescharacteristic
91M16×C131—42no—
92C2×C8×C131—22no—
93C2×C8×C131—22no—
94C2×C8×C131—41no—
95C4⋊C4×C131—22no—
96C4⋊C4×C131—22no—
97C4⋊C4×C131—21no—
98C4⋊C4×C131—21no—
99C4⋊C4×C131—22no—
100C4⋊C4×C131—22no—
101C4⋊C4×C131—41no—
102C4⋊C4×C131—41no—
103C4⋊C4×C131—41no—
104C4⋊C4×C131—41no—
105C22⋊C4×C131—41no—
106C22⋊C4×C131—41no—
107C42×C131—24no—
108C42×C131—22no—
109C42×C131—22no—
110C42×C131—42no—
111C42×C131C2×D411yescharacteristic
112C42×C131C2×D411yescharacteristic
113C42×C131C2×D411yescharacteristic
114C42×C131#4111yescharacteristic
115C23×C131—41no—
116C23×C131#12011yescharacteristic
117Q8×C131—42no—
118Q8×C131—82no—
119Q8×C131—82no—
120Q8×C131—82no—
121Q8×C131—81no—
122Q8×C131—81no—
123D4×C131—42no—
124D4×C131—42no—
125D4×C131—42no—
126D4×C131—82no—
127C2×C4×C131—22no—
128C2×C4×C131—22no—
129C2×C4×C131—24no—
130C2×C4×C131—42no—
131C2×C4×C131—42no—
132C2×C4×C131—44no—
133C2×C4×C131—41no—
134C2×C4×C131—42no—
135C2×C4×C131—42no—
136C2×C4×C131—44no—
137C2×C4×C131—81no—
138C2×C4×C131—81no—
139C2×C4×C131#12011yescharacteristic
140C2×C4×C131#12011yescharacteristic
141C2×C4×C131#12111yescharacteristic
142C2×C4×C131#12111yescharacteristic
143C2×C4×C131#12111yescharacteristic
144C2×C4×C131#12711yescharacteristic
145C2×C4×C131#13512yes—
146C2×C4×C131AGL(1,ℤ/8)12yes—
147C8×C131—42no—
148C8×C131—42no—
149C8×C131—81no—
150C22×C131—21no—
151C22×C131—21no—
152C22×C131—81no—
153C22×C131—81no—
154C22×C131—81no—
155C22×C131#39211yescharacteristic
156C22×C131#44912yes—
157C4×C131—21no—
158C4×C131—21no—
159C4×C131—44no—
160C4×C131—82no—
161C4×C131—82no—
162C4×C131—81no—
163C4×C131#45412yes—
164C4×C131#45612yes—
165C4×C131#46312yes—
166C4×C131#49511yescharacteristic
167C4×C131#49611yescharacteristic
168C2×C131—22no—
169C2×C131—161no—
170C2×C131#200311yescharacteristic
171C2×C131#200511yescharacteristic
172C2×C131#201211yescharacteristic
173#10286C13111yesmaximal, characteristic, direct product factor, Sylow
174C131#1028611yescharacteristic, direct product factor, Sylow
175#3227C2×C13111yescharacteristic
176#3226C2×C13111yescharacteristic
177#2862C2×C13111yescharacteristic, complemented
178#1962C2×C13111yescharacteristic
179#1549C2×C13111yescharacteristic, complemented
180#1546C2×C13111yescharacteristic, complemented
181#1276C2×C13111yescharacteristic, complemented
182#532C22×C13111yescharacteristic
183C2×C4⋊Q8C22×C13111yescharacteristic
184C2×C4⋊Q8C22×C13111yescharacteristic
185#500—21no—
186#498—21no—
187#486—21no—
188#486—21no—
189#481—22no—
190#480—22no—
191#476—22no—
192#474—22no—
193#431C22×C13111yescharacteristic
194#431C22×C13111yescharacteristic
195#423C22×C13111yescharacteristic
196C2×#104—22no—
197#391—22no—
198#391—22no—
199#382—22no—
200C43C22×C13111yescharacteristic
201#332—22no—
202#332—22no—
203C2×#41—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C2×M16—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8D4×C13111yescharacteristic
216#127D4×C13111yescharacteristic
217#124—21no—
218#121—21no—
219#121—21no—
220C4×D4—21no—
221C4×D4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4D4×C13112yes—
225C2×C4⋊C4D4×C13112yes—
226C2×C42—21no—
227C2×C42—21no—
228C2×C42D4×C13112yes—
229C2×C42C23×C13111yescharacteristic
230#107—24no—
231#106—24no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8D4×C13112yes—
235C4⋊C8D4×C13112yes—
236#104—44no—
237#102—24no—
238#102—24no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241C4×C8—21no—
242C4×C8—21no—
243#95—28no—
244#41—42no—
245#41—42no—
246C2×Q8—21no—
247C2×Q8—44no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4C2×D4×C13111yescharacteristic
263C22×C4C2×D4×C13111yescharacteristic
264C22×C4C2×D4×C13111yescharacteristic
265M16—42no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—41no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C42—24no—
282C42—22no—
283C42—22no—
284C42—42no—
285C42C2×D4×C13111yescharacteristic
286C42C2×D4×C13111yescharacteristic
287C42C2×D4×C13111yescharacteristic
288C42#41×C13111yescharacteristic
289C23—41no—
290C23#120×C13111yescharacteristic
291Q8—42no—
292Q8—82no—
293Q8—82no—
294Q8—82no—
295Q8—81no—
296Q8—81no—
297D4—42no—
298D4—42no—
299D4—42no—
300D4—82no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—44no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—44no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4#120×C13111yescharacteristic
314C2×C4#120×C13111yescharacteristic
315C2×C4#121×C13111yescharacteristic
316C2×C4#121×C13111yescharacteristic
317C2×C4#121×C13111yescharacteristic
318C2×C4#127×C13111yescharacteristic
319C2×C4#135×C13112yes—
320C2×C4AGL(1,ℤ/8)×C13112yes—
321C8—42no—
322C8—42no—
323C8—81no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22#392×C13111yescharacteristic
330C22#449×C13112yes—
331C4—21no—
332C4—21no—
333C4—44no—
334C4—82no—
335C4—82no—
336C4—81no—
337C4#454×C13112yes—
338C4#456×C13112yes—
339C4#463×C13112yes—
340C4#495×C13111yescharacteristic
341C4#496×C13111yescharacteristic
342C2—22no—
343C2—161no—
344C2#2003×C13111yescharacteristic
345C2#2005×C13111yescharacteristic
346C2#2012×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC2×C42C23×C131
prime radical#532×C131C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #2862×C131C2semidirect
5. #1549×C131C2semidirect
6. #1546×C131C2semidirect
7. #1276×C131C2semidirect
173. #10286C131direct (N × H)
174. C131#10286direct (N × H)
177. #2862C2×C131semidirect
179. #1549C2×C131semidirect
180. #1546C2×C131semidirect
181. #1276C2×C131semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3227×C1312
#3226×C1312
#2862×C1312
#1962×C1312
#1549×C1312
#1546×C1312
#1276×C1312
#10286131